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surface area and volume of cube ,cuboid,cylinder,cone,sphere and hemisphere.

surface area and volume of cube ,cuboid,cylinder,cone,sphere and hemisphere.

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- 1. AND VOLUMES
- 2. DEFINATION:A cuboid whose length ,breadth, height is called a cube. SOLID CUBE:A solid cube is the part of the space enclosed by six faces of the cube.
- 3. SURFACE AREA OF CUBE:Since all six faces of a cube are squares of the same size i.e. For a cube we have l=b=h. Thus, if l cm is the length of edge or side or a cube,then Therefore, surface area of a cube=6lsq
- 4. I. II. III. Lateral surface area of cube=4(edge)sq Volume of cube=(edge) cubic L.S.A of a cuboid =2 (l + b) h T.S.A of a cuboid =2(lb+bh+lh) Volume of the cuboid =lbh T.S.A of a cube =6a2< Total surface area of a cube, sum areas of all the faces of a cube >
- 5. FaceAlso called facets or sides. A cube has six faces which are all squares, so each face has four equal sides and all four interior angles are right angles. See Definition of a square. In the figure above, drag the 'explode' slider to see the faces separated for clarity. EdgeA line segment formed where two edges meet. A cube has 12 edges. Because all faces are squares and congruent to each other, all 12 edges are the same length. VertexA point formed where three edges meet. A cube has 8 vertices.
- 6. A solid which has six rectangular faces at right angles to each other.
- 7. Surface of the cuboid without the top = 2 (bh + hl) + lb SURFACE AREA OF CUBOID WITHOUT THE TOP AND THE BOTTOM = 2 (bh + hl)
- 8. AREA OF RECTANGLE 1 = (l x h) + AREA OF RECTANGLE 2 = (l x b) + AREA OF RECTANGLE 3 = (l x h) + AREA OF RECTANGLE 4 = (l x b) + AREA OF RECTANGLE 5 = (b x h) + AREA OF RECTANGLE 6 = (b x h) = 2 (l x b) + 2 (b x h) + 2(l x h) = 2 (lb + bh + hl)
- 9. Volume is the space occupied by an object. Volume is also referred to capacity of an object. THUS, VOLUME OF CUBOID = BASE AREA x HEIGHT = (l x b) x h =lxbxh VOLUME OF CUBOID = l x b x h
- 10. A cylinder is one of the most basic curvilinear geometric shapes, the surface formed by the points at a fixed distance from a given line segment, the axis of the cylinder. The solid enclosed by this surface and by two planes perpendicular to the axis is also called a cylinder.
- 11. TSA of a cylinder = area of the base + area of top + CSA of the cylinder = ∏r2 + ∏r2 + 2∏rh = 2∏r2 + 2∏rh = 2∏r(r + h) Where, r is the radius h is the height of the cylinder
- 12. Volume of the cylinder = area of the base x height = r2 x h = ∏r2h Volume of hollow cylinder = ∏(R2 - r2) h Where, r is the radius and h is the height
- 13. A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (usually circular) to a point called the apex or vertex.
- 14. when we cut a cone from its slant height curved surface area of cone =area of sector =1/2 *l *(2 ∏r) = ∏r l
- 15. TOTAL SURFACE AREA =curved surface area +area of the base = ∏rl+ ∏r2 + = ∏r(r+l)
- 16. WHEN WE TAKE A CONE AND A CYLINDER OF SAME HEIGHT AND RADIUS WE GET
- 17. 1. A sphere is a perfectly round geometrical object in three-dimensional space. Like a circle, which is in two dimensions in a mathematical sense, a sphere is the set of points that are all the same distance r from a given point in threedimensional space. This distance r is the radius of the sphere, and the given point is the center of the sphere. The maximum straight distance through the sphere passes through the centre and is thus twice the radius; it is the diameter. 2. Hemisphere refers to the equal halves of the sphere and can also be called the 3d design for a semi-circle.
- 18. When we talk about painting or polishing the surface it is related to the surface area. Surface-Area (TSA) = 4∏r2 Where, ‘r’ is the radius from the center to surface.
- 19. TSA of hemisphere = 3∏r2 CSA of hemisphere = 2∏r2 Where, ‘r’ is the radius.
- 20. When we talk about the air in the solid or want to count the no. of small object from the bigger one then it is related to the volume. Volume of the sphere = 4/3∏r3 Where, r is the radius.
- 21. Volume of the Hemisphere = 2/3∏r3 Where, r is the radius.
- 22. Cube – by Stuti Somani Cuboid –by Niriksha Mogaveera Cylinder – by Aditya Warrior Cone – by Shreyans Maliwal Sphere and Hemisphere-by Pakshal Animation– by Shreyans Maliwal Shah

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